Geometrical Modulated Model Predictive Control With Current Limiting for Power Converters

This article introduces a method called geometrical modulated model predictive control (GM2PC) for three-phase power converters. Its objective is to guarantee voltage synthesis, current limiting, fixed switching frequency, no need for weighting factors or cascaded control structure, and fast dynamic response, while also addressing overmodulation issues and distributing PWM signals in cascaded H-bridge (CHB) multilevel converters in a simple and efficient manner. A convex optimization problem is formulated using a discrete-time model to minimize the output tracking error in a three-phase converter connected to an LC output filter. This formulation includes two quadratic constraints and takes into account external disturbances. To solve this problem, the constraints are treated as circular areas within the space vector diagram for current limitation and voltage synthesis. The Karush–Kuhn–Tucker (KKT) conditions are applied to obtain an unconstrained solution that identifies the mode of operation, which is used to geometrically find an optimal solution. Unlike conventional quadratic minimization algorithms, the proposed method does not require recursive solutions nor the analysis of all vectors or sectors in the space vector diagram, reducing significantly the computational burden. The method is validated for a five-level CHB, and the results demonstrate its efficiency and fast control algorithm.